NCERT Class 11 Chapter 6 Maths Linear Inequalities MCQ

NCERT Class 11 Chapter 6 Maths Linear Inequalities MCQ | Questions & Answers: Give a try for the NCERT Class 11 Chapter 6 Maths Linear Inequalities MCQ Quiz. And know how much capable you are of solving the problems. Good luck!

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1. The solution set of inequality 2x/x²-9 ≤ 1/x+2

A. (-∞, - 2)∪(3, ∞)

B. (-∞, -3)∪(-2, 3)

C. (-3, 0]∪(3, ∞)

D. none of these

2. The number of integral solutions of x+2 / x²+1 >1/2

A. 4

B. 5

C. 3

D. none of these

3. The least integer a, for which
1 log5 (x² + 1) ≤ log5 (ax² + 4x + a) is true for xεR all

A. 6

B. 7

C. 10

D. 1

4. Consider the following statements about Linear Inequalities :
(1) Two real numbers or two algebraic expressions related by the symbols <, >, ≤ or ≥ form an inequality.
(2) Equal numbers may be added to (or subtracted from) both sides of an inequality.
(3) Both sides of an inequality can be multiplied (or divided) by the same positive number.
Which of the above statements are true ?

A. only (1)

B. only (2)

C. only (3)

D. all the above

5. Solutions of the inequalities comprising a system in variable x are represented on number lines as given below, then

A. x Î(-∞,- 4]∪[3,∞)

B. x Î[-3,1]

C. x Î(-∞,-4)∪(3,∞)

D. x Î[-4,3]

6. x and b are real numbers. If b > 0 and |x| > b, then

A. x Î(-b,∞)

B. x Î(-∞,b)

C. x Î(-b,b)

D. x Î(-∞,-b)∪(b,∞)

7. If x is real number and |x| < 3, then

A. x ≥ 3

B. –3 < x < 3

C. x ≤ -3

D. -3 ≤ x ≤ 3

8. The values of x satisfying | x – 4 | + | x – 9 | = 5, is :

A. x = 4, 9

B. 4 ≤ x ≤ 9

C. x ≤ 4 or x ≥ 9

D. none of these

9. The set of real values of x for which log 0.2 x+2/x ≤ 1 is

A. (-∞, -5/2]∪(0, ∞)

B. [5/2, ∞)

C. (-∞, - 2)È[0, ∞)

D. none of these

10. The solution set of the inequality
5 x+2 >(1/25)^1/x is

A. (-2, 0)

B. (-2, 2)

C. (-5, 5)

D. (0, ∞)

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11. Given that x, y and b are real numbers and x < y , b < 0, then

A. x/b < y/b

B. x/b ≤ y/b

C. x/b > y/b

D. x/b ≥ y/b

12. The integral value of x which satisfies the inequality x⁴ - 3x³ - x + 3 < 0 is

A. 0

B. 1

C. 2

D. 3

13. Solution of a linear inequality in variable x is represented on number line. Choose the correct answer from the given four options.

A. x Î(-∞,5)

B. x Î(-∞,5]

C. x Î[5,∞)

D. x Î(5,∞)

14. The solution set of the inequality 1/x < is

A. (1, ∞)

B. (-∞, 1)

C. (-∞, 0)∪(1, ∞)

D. none of these

15. 8x² + 16x - 51 /(2x-3)(x+4) > 3, if x satisfies

A. x < –4

B. –3 < x < 3/2

C. x > 5/2

D. all the above

16. The equation
| x + 1|log(x+1) (3+2x - x2) = (x-3) | x | has

A. unique solution

B. two solution

C. no solution

D. More than two solutions

17. The solution set of the equation 4{x} = x +[x], where {x} and [x] denote the fractional and integral parts of a real number ‘x’ respectively, is

A. { 0}

B. {0, 5/3}

C. [0, ∞)

D. none of these

18. The equation x +1 - x -1 = 4x -1 has

A. no solution

B. one solution

C. two solution

D. more than two solutions

19. The values of x satisfying the inequality | x³ -1| ≥ 1- x belong to

A. (-∞, -1]

B. (-∞,-1]∪[0,∞)

C. [1, ∞)

D. none of these

20. The number of ordered pairs (x, y) satisfying 3^x ×5^y = 75 and 3^y ×5^x = 45 is

A. 0

B. 1

C. 3

D. none of these

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21. The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160 cm, then what can you say about breadth?

A. breadth = 20

B. breadth ≤ 20

C. breadth ≥ 20

D. breadth ≠ 20

22. Let C/5 = F-32/9 . If C lies between 10 and 20, then :

A. 50 < F < 78

B. 50 < F < 68

C. 49 < F < 68

D. 49 < F < 78

23. The set of real values of x satisfying
| x -1|≤ 3 and | x -1|≥1 is

A. [2, 4]

B. (-∞, 2]∪[4, +∞)

C. [-2, 0]∪[2, 4]

D. none of these

24. The solution set of x² - 3x + 4 /x+1 > 1,x ε R is

A. (3, +∞)

B. (-1, 1)È(3, +∞)

C. [-1, 1]È[3, +∞)

D. none of theses

25. If k ≠ [0, 8], find the value of x for which the inequality x² k² / k (6 x) ≥ 1 is satisfied.

A. –1 < x < 1

B. –1 < x < 2

C. –2 < x < 1

D. –3 < x < 1